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Rational Exponents and Radicals: Simplify, Evaluate, and Solve Equations

Learn how to simplify and evaluate expressions with rational exponents, simplify radical expressions, and solve equations involving radicals. Practice solving problems and improve your understanding of rational exponents and radicals.

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Rational Exponents and Radicals: Simplify, Evaluate, and Solve Equations

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  1. Section 7.1 Rational Exponents and Radicals

  2. Find the nth root of a number, if it exists. A OBJECTIVES

  3. Evaluate expressions containing rational exponents. B OBJECTIVES

  4. Simplify expressions involving rational exponents. C OBJECTIVES

  5. DEFINITION NTH ROOT If a and x are real numbers and n is a positive integer: x is an nth root of a if xn = a

  6. DEFINITION PRINCIPLE NTH ROOT

  7. DEFINITION RATIONAL EXPONENTS AND THEIR ROOTS

  8. DEFINITION RADICAL EXPRESSION WITH AN M/N EXPONENT

  9. LAWS OF EXPONENTS If r, s, and t are rational, and a and b are real:

  10. LAWS OF EXPONENTS If r, s, and t are rational, and a and b are real:

  11. Practice Test Chapter 7Section 7.1A Exercise #1

  12. Find, if possible.

  13. Find, if possible.

  14. Practice Test Chapter 7Section 7.1B Exercise #4

  15. Evaluate if possible.

  16. Evaluate, if possible.

  17. Section 7.2 Simplifying Radicals

  18. Simplify radical expressions. A OBJECTIVES

  19. Rationalize the denominator of a fraction. B OBJECTIVES

  20. Reduce the order of a radical expression. C OBJECTIVES

  21. DEFINITION nTH ROOT

  22. LAWS For Simplifying Radical Expressions

  23. LAWS For Simplifying Radical Expressions

  24. LAWS For Simplifying Radical Expressions

  25. DEFINITION

  26. DEFINITION

  27. Practice Test Chapter 7Section 7.2A Exercise #7b

  28. Simplify.

  29. Practice Test Chapter 7Section 7.2A Exercise #8b

  30. Simplify.

  31. Practice Test Chapter 7Section 7.2A Exercise #9b

  32. Simplify.

  33. Section 7.3 Operations with Radicals

  34. Add and subtract similar radical expressions. A OBJECTIVES

  35. Multiply and divide radical expressions. B OBJECTIVES

  36. Rationalize the denominators of radical expressions involving sums or differences. C OBJECTIVES

  37. DEFINITION LIKE RADICAL EXPRESSIONS Radical expressions with the same index and the same radicand.

  38. DEFINITION CONJUGATE The expressions a + b and a – b are conjugates of each other.

  39. Practice Test Chapter 7Section 7.3A Exercise #14

  40. Perform the indicated operations.

  41. Perform the indicated operations.

  42. Practice Test Chapter 7Section 7.3B Exercise #16b

  43. Perform the indicated operations.

  44. Practice Test Chapter 7Section 7.3B Exercise #18b

  45. Find the product.

  46. Practice Test Chapter 7Section 7.3C Exercise #20

  47. Rationalize the denominator.

  48. Section 7.4 Solving Equations Containing Radicals

  49. Solve equations involving radicals. A OBJECTIVES

  50. Solve applications requiring the solution of radical equations. B OBJECTIVES

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